Current stereo headsets of a necklace, collar or neck loop type have predominantly two types of connection between earphones and the neck loop: headsets with two side nodes, in which earphone cords are connected with the neck loop and not connected between themselves, and headsets with a single back node, in which earphone cords are connected to each other and to the neck loop in the single node.
A conventional headset comprises earphones that are connected through cords to a supporting structure, which accommodates a signal transceiver and is connected to a necklace (neck loop) (U.S. Pat. No. 7,416,099 B2, publ. 26 Aug. 2008).
The headset comprises long unsecured sections of cords connecting the earphones with the neck loop, because the additional length is needed when the user rotates and moves the head relative to the torso. The headset has two nodes and the length of the movable portion of the cords in the headset is more than 19 cm. The cords hang freely along the entire length thereof in the air over the body surface, so they are slacking and may tangle and cling to surrounding objects. In addition, the headset is difficult to wear under clothing, in both operational and non-operational state, i.e. when the earphones are taken off.
An earphone storage structure comprises a necklace (analog of neck loop), two fasteners formed in the two ends of the necklace, and stoppers (U.S. Pat. No. 7,936,895 B2, publ. 3 May 2011). The size of the fasteners is less than the size of the stoppers and the size of the earphones, therefore the earphones may be pulled out when they are not used. The stoppers are actually connection nodes, and this device relates to headsets with two side nodes. The earphone storage structure has the same limitations as the previous device: cords are slacking, and the structure is difficult to wear under clothing and managing it over clothing.
A lanyard for a portable electronic device (U.S. Pat. No. 7,650,007 B2, published 19 Jan. 2010) comprises two side connection nodes and allows adjusting the length of earphone cords, but the lanyard does not eliminate sagging of cords in operational state.
In a necklace-type audio device (WO 2012/015257 A1, publ. 2 Feb. 2012), earphone cables form a neck loop when they are attached at the ends to a jack disposed on the user's chest, and crossed through two rings disposed in the back of the necklace (neck loop), the rings being adapted to adjust the length of the neck loop and earphone cables. In this device, the length of the cords connecting an earphone to the necklace (neck loop) is even longer than in necklace-type headsets with two side nodes; this fact contributes to slacking the cords, and peculiarities of adjusting the lengths of cords in the headset eliminates the possibility of wearing it under clothes.
Therefore, the conventional devices, first, comprise excessively long unsecured sections of cords that connect the head part of a headset with a neck loop (in headsets with a single node the length of freely hanging cords is about 19 cm, and in headsets with two side units it is about 25 cm) and, second, unsecured sections of cords in the conventional devices do not fit to the body surface. The cord slack cannot be fully removed without restricting the freedom of movement of the user's head. Therefore, when the devices are used the cords either slack, tangle and cling to surrounding objects, or restrict the freedom of movement.
Therefore, no constant wear device has been designed up to the present moment, which would have a small total length of freely hanging cords snuggly fitted to the body and creating no obstacles to movements of the head. Provision of such a device could improve the ease of use, secure fixation to the user's body, and prevent failures caused by the cords clinging with surrounding objects.
In general, slacking of cords depends on the following factors:
the length of movable portion of cords between fixed points; in all conventional neck headsets this is the length of cord from an earphone to the neck loop, so the shorter the movable portion of the cord, the less is the slack;
cord tension;
degree of adherence of the cord to the body surface;
position of the cords; cords disposed on a plane do not slack as opposed to cords hanging in the air or lying above natural depressions on the surface of user's body.
Impact of the above factors is illustrated in the drawings and is explained below on examples of conventional devices and a device according to the invention.
Basis for the inventive structure of a headset
for a mobile electronic device
When a user wears a headset (FIG. 1) in the form of a neck loop, a node that connects earphone cords 5 to a neck loop 1 rests on the dorsal surface of the user's neck, in the region of the seventh cervical vertebra. Slightly lower on the human body there is a trough deepening lying between the spinous and transverse processes of the vertebrae, sulcus dorsalis, at the level of the second-third thoracic vertebrae in the interscapular region, where a depression of various intensity of about 4×5 cm (depending on the constitution and development of subcutaneous fat) is formed at the place of attachment on the medial edges of both blades of serratus anterior muscle, and a large and minor rhomboids muscles (musculae rhomboidei major et minor). The depression may receive a cord winding mechanism and an earphone storage pocket, without projecting above the surface of the body and so without causing inconvenience to the user.
From the cord connection node on the neck loop the cords run up on the dorsal surface of the neck to the back of the head, on the paravertebral deepening, sulcus costae vertebralis major, not reaching the outside occipital protuberance at the level of the first-second cervical vertebrae, where an additional cord connection node, suboccipital node 6, is appropriate to arrange. If the cords are directed in V manner from the suboccipital node in the oblique anterior-upward direction slightly above or at the hairline, which is almost coinciding with the upper occipital skull line, through the mastoid regions (regiones mastoideae) of the neck, above the mastoid processes, through the projection of ligamentum auriculare superior, which attaches the top part of the auricular cartilage to the squamous part of the temporal bone on the upper section of the auricle between the front curl and tragus of the outer ear to a fixation point in the earphone 3 of the appropriate side, then the stable position of the suboccipital cord connection node will be provided by the availability of fixing anatomical structures at the datum point, such as the external occipital protuberance and lateral occipital projections, while a snug fit of the cords on the scalp is provided by stretching them on the dorsal surface of the head and neck in the places where the cords pass like a girth due to the partial hook-like overlap of the earphone cords through the ligamentum auriculare with additional fixing of the earphones inside the auricle.
With such attachment only the cords in the section 7 between nodes 5 and 6 are movable, and only this section may have a slack to compensate for the cord length, which changes when the head turns in the horizontal plane, tilts back, rocks from side to side, as well as when the movements are combined, that is, in all options that can arise in closed kinematic chains of the neck.
Cords 4 are relatively snug fitted to the scalp and fixed relative to the user's head, and their length does not vary at all the above movements and varies so little that these variations can be neglected.
Adherence and immobility of the cords 4 between the nodes are also promoted by the cellular connective tissue structure of the subcutaneous fat of the occipital region, a minor displacement of the skin in the area, the presence of Langer's lines running in the transverse direction in the skin, as well as the passage of the cord on a hollow of the postaural cavity, the hook-like overlap of the cords and positioning the earphones in the outer ear.
In conjunction with the suboccipital node the tension and absence of slack are further provided by the design of the used earphone, which is placed inside the auricle, in most cases, without arc, but having a stiff part—an earphone arm attached to the earphone body lying in the outer ear and continued upward from the helical root on the ascending part of the helix to the ligamentum auriculare superior, the attachment point of the top of the auricle to the temporal bone. A flexible cord extends from the stiff arm, leaning over the above ligamentum auriculare superior at an angle of less than 45°, which contributes to the fact that the rigid arm of the earphone forms a lever, where at accidental tearing off of the earphone cords, that is, when the cords are pulled at down and back tension vector, the arising moment abuts the earphone against the tragus, thereby fixing the earphone between the tragus and the external auditory canal.
In terms of biomechanics it should be noted that movements of the head are described on the basis of closed kinematic patterns, and extrapolation of even fairly complex combinations of head movements to the fixation points can be considered in only one narrative category—as lengthening-shortening the cord section between the dorsal cord connection node on the neck loop and the cord connection suboccipital node, which is almost stationary relative to the head and lies under the outer posterior occipital protuberance.
To construct a closed kinematic model, a headset can be represented as consisting of two basic parts and a movable connection thereof (FIG. 1).
A first part (head part) is stationary relative to the user's head, comprises two earphones 3, two earphone cords 4 enveloping the auricle from above, and a suboccipital node 6.
A second part is stationary relative to the user's body, comprises a neck loop 1 and a cord connection node disposed on the neck loop on the dorsal surface of the neck, a dorsal node 5.
As shown in FIG. 1, positions of the cord connection nodes has been chosen at reference numeral 5, point A (FIG. 2) and reference numeral 6, point B (FIG. 2). In this case, the length of the free-hanging cord 7 in the section between the nodes should be minimal.
To determine the length of the AB section, variations in the distance between points A and B when the head turns are to be considered. In this case, “distance” is the length of the geodesic line connecting points A and B on the surface of the neck (FIG. 2b). First, define the extension of the cord when the head rotates sideways. Maximum angle of rotation of the head is 90°. Determine the AB distance.
To determine the length of the geodesic line it is necessary to describe mathematically the surface of the neck and possible movements of the head and neck. The neck surface can be represented with sufficient accuracy as a cylinder (FIG. 2a). Head and neck can make the following motions: bending-tilting forward, extension/tilting backward, abduction and adduction/tilting to the left and to the right, turns to the left and to the right. High mobility of the cervical spine is due to its segmentation: having a height of about 13 cm, it contains seven medium-sized vertebrae and six high intervertebral discs. Between the first cervical vertebrae and the occipital bone, in the atlantal-occipital joint, adduction/abduction and flexion/extension of the head are performed, and between the first and second cervical vertebra turns of the head to the right and the left are performed. The joint work of these joints provides the head movement about three axes. Thus, combined movements of the head and neck are made in relation to the body, while independent movements of the head are made in relation to the neck. This is because the cervical spine is very flexible, and independent movements are possible between the first and second cervical vertebrae.
Consider the behavior of the kinematic model of the headset when the head rotates in the horizontal plane.
When the head rotates in the horizontal plane the neck twists mainly in the region between the first and second vertebrae. Moreover, since the cervical spine is located closer the back of the neck, the twisting axis is also close to the back surface of the cylinder. Since the twisting is performed only in the upper part of the cylinder about a non-central axis, the cylinder surface is distorted. The distortion is most strongly manifested in the region of the first and second cervical vertebrae, just where point B lies. The main part of the geodesic line passes below the distortion, so in the calculations we assume the surface as cylindrical. An important issue is the determination of the position of point B when the upper part of the cylinder is twisted to a maximum angle α=π/2. Since ears are symmetric about the twisting axis, that is the axis of the vertebral column, and the point B is fixed by the taut cords in symmetrical position as well, the position of point B can be expected in the next central angle φ (FIG. 2b).
                    φ        =                  arcsin          ⁡                      (                                          R                -                D                            R                        )                                              (        1        )            
The height of point B will not change at rotation either because it is fixed by the taut earphone cords.
Consider the task of geodesic line of a cylinder having base radius R and height h (FIG. 2b). The line passes through two diametrically opposite points on different basis.
It's the differential of geodesic line:ds=√{square root over (dx2+dy2+dz2)}
Since the curve lies on the surface of the cylinder, it is convenient to use cylindrical coordinates, with dx2+dy2=R2dφ2, where φ is the polar angle (FIG. 2b). In polar coordinates, the task reduces to finding dependence z(φ), at which the length of the curve is minimal or the functional:
                    S        =                              ∫            0                          φ              0                                ⁢                                                                      R                  2                                +                                  z                                      ′                    ⁢                                                                                  ⁢                    2                                                                        ⁢                                                  ⁢                          ⅆ              φ                                                          (        2        )            
is minimal.
From the calculus of variations it is known that minimum is reached for the curve that satisfies the Euler equation, in this case:
                                          (                                          z                ′                                                                                  R                    2                                    +                                      z                                          ′                      ⁢                                                                                          ⁢                      2                                                                                            )                    ′                =        0                            (        3        )            
It follows that z′(φ)=a, where a is the constant factor, then z(φ)=a×φ+b. Coefficients are determined though boundary points A (R,0,0), the attachment point of the lower clip, and B(R, φ0, h) with the polar angle φ=0 being at point A and equal to φ0 at point B. Then the coefficients are of the form: a=h/φ0, b=0. Then z(φ)=φ×h/φ0. And the length of the curve is equal to the value of the functional, i.e.:
                                                        S              =                            ⁢                                                ∫                  0                                      φ                    0                                                  ⁢                                                                                                    R                        2                                            +                                                                        h                          2                                                /                                                  φ                          0                          2                                                                                                      ⁢                                                                          ⁢                                      ⅆ                    φ                                                                                                                          =                            ⁢                                                                                          φ                      0                      2                                        ⁢                                          R                      2                                                        +                                      h                    2                                                                                                          (        4        )            
Thus, variation in distance AB or mobility of cords ΔS is:ΔS=√{square root over (h2+R2φ02)}−h  (5)
With regard to expression (1) get the expression for mobility of cords:
                              Δ          ⁢                                          ⁢                      S            t                          =                                                            h                2                            +                                                R                  2                                ⁢                                                      arcsin                    2                                    ⁡                                      (                                                                  R                        -                        D                                            R                                        )                                                                                -          h                                    (        6        )            
Now consider for comparison variation in the length of cords at horizontal rotation of the head in conventional headsets. FIG. 3a shows an example of such a headset. In this case, cords are clamped at point A, and the movable part is the entire cord from point A to earphones disposed at points C and D. Conventionally denote the headset as a single node headset. Thus, mobility of the cords can be determined from the difference between the distances from point A and D when the head rotates at the angle of 90° in one direction and in the other direction, since while the distance or the geodesic line length increases in one direction, it decreases in the other direction. These two distances can be determined in FIG. 3b, where a minimum distance is the length of line AC, and a maximum distance corresponds to line AD. As a result, mobility of the cords can be found from the expression (5) with the assumption of h=H and φ0=π, and it has the form:ΔSt1=√{square root over (H2+R2π2)}−H  (7)
Consider another type of a headset, which will be conventionally called a headset with two side nodes (FIG. 4a). In this case assume that the headset cord, at rotation, always passes through points at the base of the cylinder, i.e. points A and B, cord connection nodes. Then the minimum distance between points A and C or B and D is H. The maximum distance when the head is rotated to 90° is shown by geodesic lines AC and BD (FIG. 4b). As a result, mobility of the cords is also determined from expression (5) with the assumption of h=H and φ0=π/2, and is defined by the following expression:ΔSt2=√{square root over (H2+R2π2/4)}−H  (8)
Next, consider behavior of the kinematic model when the head tilts forward and backward in the vertical plane.
Tilts of the head are performed by rotation of the head around the axis passing between the first cervical vertebra and the occipital bone. The tilt is often accompanied by a tilt of the entire cervical spine. In a headset with two nodes the tilt of the neck has a little effect on distance AB, but rotation of the head has a significant impact, since node B is disposed directly on the occipital part. Thus, knowing distance from B to axis of rotation r and angle of rotation α (5a), shift of node B can be estimated asBB0=rα  (9)
Obtain an expression for the length of segment AB at arbitrary angle α from the triangle AOB (FIG. 5b):AB2=AO2+r2−2AO×r×cos(α+β)  (10)
Distance to axis r can be determined though the distance from the back surface of the neck to the center of the cervical spine, i.e. R-D, and the difference of heights of point B and the axis of rotation of the head h0:r=√{square root over ((R−D)2+h02)}  (11)
From triangle OO1A obtain the following expression:AO=√{square root over ((R−D)2+(h+h0)2)}{square root over ((R−D)2+(h+h0)2)}  (12)
Expression for angle β can be obtained from expressions (10), (11) and (12) by substituting α=0, AB=h.
                    β        =                  arccos          ⁢                                                                      (                                      R                    -                    D                                    )                                2                            +                              hh                0                            +                              h                0                2                                                                                      (                                                                                    (                                                  R                          -                          D                                                )                                            2                                        +                                                                  (                                                  h                          +                                                      h                            0                                                                          )                                            2                                                        )                                ⁢                                  (                                                                                    (                                                  R                          -                          D                                                )                                            2                                        +                                          h                      0                      2                                                        )                                                                                        (        13        )            
Thus, the expression for the AB has the form:
                    ⁢          (      14      )                  AB      ⁡              (        α        )              =                                                                                        2                  ⁢                                                            (                                              R                        -                        D                                            )                                        2                                                  +                                                      (                                          h                      +                                              h                        0                                                              )                                    2                                +                                  h                  0                  2                                -                                                                                        2                ⁢                                                                            (                                                                                                    (                                                          R                              -                              D                                                        )                                                    2                                                +                                                                              (                                                          h                              +                                                              h                                0                                                                                      )                                                    2                                                                    )                                        ⁢                                          (                                                                                                    (                                                          R                              -                              D                                                        )                                                    2                                                +                                                  h                          0                          2                                                                    )                                                                                                          ⁢                  cos          ⁡                      (                          α              +              β                        )                              
It should be noted that in case of tilting the head backward expression (14) is no longer true, because there is no tension of the skin and soft tissues of the dorsal part of the neck. In this case it is appropriate to estimate distance BB0 as the difference between heights of points B and B0.Δh=r(cos(γ0+α)−cos γ0)  (15)
As a result, mobility of the cords is calculated from expression {14) by substituting α=αm (maximum tilt angle), and (15) by substituting α=αm:
                              Δ          ⁢                                          ⁢                      S            c                          =                              AB            ⁡                          (                              α                m                            )                                -                                                                                          (                                          R                      -                      D                                        )                                    2                                +                                  h                  0                  2                                                      ⁢                          (                                                cos                  ⁡                                      (                                                                  γ                        0                                            -                                              α                        m                                                              )                                                  -                                  cos                  ⁢                                                                          ⁢                                      γ                    0                                                              )                                                          (        16        )            
Apparently, αm cannot exceed γ0 due to the limit on deformation of the neck. To assess mobility of the cords we may assume αm=γ0, then with regard to expression (14) obtain:ΔSc=AB(γ0)−√{square root over ((R−D)2+h02)}(1−cos γ0)  (17)
In case of headsets with a single node or with two side nodes rotation in the vertical plane affects the height of points C and D. Variation in the latter, Δh0, can be determined if relative distance r0 between axis CD and the axis of rotation, as well as angular position α0 of the axes are known (FIG. 6a):Δh0=r0(cos α0−cos(α0+α))  (18)
As a result, variation in the distance or mobility of cords for a headset with a single node can be obtained from formula (4) with H−Δh0 set instead of h and φ=π/2. In this case, angle α varies in the range −αm<α<αm, and the height varies in the range:
                                                                        Δ                ⁢                                                                  ⁢                                  h                  01                                            =                            ⁢                                                                    r                    0                                    ⁡                                      (                                                                  cos                        ⁢                                                                                                  ⁢                                                  α                          0                                                                    -                                              cos                        ⁡                                                  (                                                                                    α                              0                                                        -                                                          α                              m                                                                                )                                                                                      )                                                  <                                                                                                      ⁢                                                Δ                  ⁢                                                                          ⁢                                      h                    0                                                  <                                                      r                    0                                    ⁡                                      (                                                                  cos                        ⁢                                                                                                  ⁢                                                  α                          0                                                                    -                                              cos                        ⁡                                                  (                                                                                    α                              0                                                        +                                                          α                              m                                                                                )                                                                                      )                                                                                                                          =                            ⁢                              Δ                ⁢                                                                  ⁢                                  h                  02                                                                                        (        19        )                                                          ⁢                              Δ            ⁢                                                  ⁢                          S                              c                ⁢                                                                  ⁢                1                                              =                                                                                          (                                          H                      -                                              Δ                        ⁢                                                                                                  ⁢                                                  h                          01                                                                                      )                                    2                                +                                                      R                    2                                    ⁢                                                            π                      2                                        /                    4                                                                        -                                                                                (                                          H                      -                                              Δ                        ⁢                                                                                                  ⁢                                                  h                          02                                                                                      )                                    2                                +                                                      R                    2                                    ⁢                                                            π                      2                                        /                    4                                                                                                          (        20        )            
FIG. 6b illustrates the case of a headset with two side nodes. Mobility of the cords can be estimated through variation in heights of points C and D. Then, from expression (19) obtain mobility of the cords in the following form:ΔSc1=Δh02−Δh01  (21)
Like the case of a headset with two nodes, estimates αm=γ0=α0 are true. Then obtain the following estimates for mobility of cords:
                              Δ          ⁢                                          ⁢                      S                          c              ⁢                                                          ⁢              1                                      =                                                                                                                                                (                                                  H                          +                                                                                    r                              0                                                        ⁡                                                          (                                                              1                                -                                                                  cos                                  ⁢                                                                                                                                          ⁢                                                                      γ                                    0                                                                                                                              )                                                                                                      )                                            2                                        +                                                                  R                        2                                            ⁢                                                                        π                          2                                                /                        4                                                                                            -                                                                                                                                                    (                                              H                        -                                                                              r                            0                                                    ⁡                                                      (                                                                                          cos                                ⁢                                                                                                                                  ⁢                                                                  γ                                  0                                                                                            -                                                              cos                                ⁢                                                                                                                                  ⁢                                2                                ⁢                                                                                                                                  ⁢                                                                  γ                                  0                                                                                                                      )                                                                                              )                                        2                                    +                                                            R                      2                                        ⁢                                                                  π                        2                                            /                      4                                                                                                                              (        22        )                                          Δ          ⁢                                          ⁢                      S                          s              ⁢                                                          ⁢              2                                      =                              r            0                    ⁡                      (                          1              -                              cos                ⁢                                                                  ⁢                2                ⁢                                                                  ⁢                                  γ                  0                                                      )                                              (        23        )            
Also consider behavior of the kinematic model when the head tilts sideway in the vertical plane.
When the head tilts sideway the movement of the head can be represented as rotation of the upper part of a cylinder about axis s, which passes approximately through point O of intersection of axes t and c.
In the case of a headset with two nodes such rotation is accompanied by a shift of point B, which can be estimated through the distance to axis of rotation O1B0 (FIG. 7a). As seen in FIG. 7b: O1B0=h0. To determine the length of AB it is necessary to determine horizontal shift Δs and vertical shift Δh of point B, because AB=√{square root over ((h+Δh)2+Δs2)}. In this case Δh=h0(1−cos α) and Δs=h0 sin α. Then mobility of section AB when the head tilts sideway will changed to maximum angle αm:ΔSs=√{square root over ((h+h0(1−cos αm))2+h02 sin2αm)}−h  (24)
Now consider the case of a headset with side nodes. In this case, variation in segments AC and BD can be accounted for by considering the shift of points C and D on arcs of circle from points C0 and D0. The length of AC in the case of the head tilt shown in FIG. 7b can be found as:AC=AC0+Rsα=H+Rsα  (25)
Here Rs is the radius of rotation trajectory about axis s, which can be found from triangle COO2, where OO2 can be found, given that the height of point O is h+h0 (FIG. 5b), then OO2=H−h−h0, and CO2=R, therefore:CO=Rs=√{square root over ((H−h−h0)2+R2)}  (26)
To determine BD only variation in the height of point D, ΔH=Rs sin α, should be taken into account because the cord in this area is loose:BD=H−ΔH=H−R sin α  (27)
Considering maximum deflection angle αm=45° the following expression can be obtained for mobility of cords:ΔSs2=Rsαm+R sin αm  (28)
Now consider the case of a headset with a single node (FIG. 8). In this case, the calculation is more complicated and requires special treatment for the length of geodesic line AC. In this task the surface of the neck can be described as a surface of an inclined cylinder. To do this, find the angle of inclination of the cylinder surface, β. From triangles BCC0 and OCCO0 find CC0=2Rs sin(α/2);
                    BC        =                                            H              2                        +                          4              ⁢                                                          ⁢                              R                s                2                            ⁢                                                sin                  2                                ⁡                                  (                                      α                    /                    2                                    )                                                      -                          4              ⁢                                                          ⁢                              HR                s                            ⁢                              sin                ⁡                                  (                                      α                    /                    2                                    )                                            ⁢                              sin                ⁡                                  (                                                            α                      /                      2                                        -                    γ                                    )                                                                                        (        29        )            
From BCC0 obtain:BC/sin(π/2−α/2+γ)=2Rs sin(α/2)/sin βso obtain:β=arcsin(2Rs sin(α/2)cos(α/2−γ)/BC)  (30)Hereγ=arctan(R/(H−h−h0))  (31)Therefore,AC=√{square root over ((BC(1−sin β))2+π2R2 cos2β/4)}  (32)
It should be noted that, taking into account the dependence of BC and β on angle α from equations (29) and (30), we can expect a nonmonotonic dependence of the line length AC(α). FIG. 9 shows this dependence for parameters listed in Table 1. It can be seen that AC reaches maximum ACmax=16.6 cm at angle α0=8.6o.
Now find the length of AD because this line describes the minimum length of the cord. In this case we may consider that the height of the cylinder has changed to ΔH=Rs sin α, then using the expression (27) obtain:AD=√{square root over ((H−Rs sin α)2+π2R2/4)}  (33)
As a result, mobility of cords ΔSs1 is determined as the difference of the lengths of lines ACmax and AD at the maximum angle of inclination, αm:ΔSs1=ACmax−√{square root over ((H−R sin αm)2+π2R2/4)}  (4)
Table 1 shows the comparison of cord mobility for various types of headsets. As seen in the table, a headset with two nodes, that is a headset, in which two earphone cords are connected to the neck loop through a dorsal cord connection node in close proximity to each other and have an additional point of fixation to each other, a suboccipital node; the cords have the lowest mobility as compared with conventional headsets. This advantage applies to all kinds of movements of the head. Comfortable wear of the headset is determined by the maximum possible mobility of cords, respectively, the difference between the minimum and maximum possible length of loose cord, arising at different positions of the head. In a headset with two nodes the maximum length is determined by maximum distance AB between the nodes, that is the length AB defined in expression (14). In a headset with a single node, the maximum length of the cord is achieved when the head rotates to 90°:Lmax 1=√{square root over (H2+R2π2)}  (35)
For a headset with two side nodes obtain the maximum length when the head tilts sideway:Lmax 2=H+Rsαm  (36)
Table 1 contains numerical estimates, from which it follows that the headset with two nodes has a minimum length of a maximum extended, but slack portion of cord. It should also be noted that the estimates obtained for a headset with two side nodes have been deliberately reduced, because cords passing from points A and B to the transceiver are not taken into account, and account of them would significantly increase Lmax2.
Therefore, the availability of two optimally positioned nodes A and B contributes not only to reduction in slacking of the cords, but also provides tension of the cords emanating from node B to earphones. Since these cords lie on the curved surface of the neck, the tension creates a pressure on the skin (FIG. 10). As a result of this pressure there arises a friction force of the cord against the skin and a pressure force of the suboccipital cord connection node, node B, against soft tissues, while the difference of vectors of these forces leads to fixation of the cords on the scalp and further secures earphones in the auricle. Thus, the fastening force is concentrated not only on the auricles, and not only by fixing the earphones in the external auditory canal, but it is uniformly distributed over the entire length of the cord, which greatly facilitates wearing of the earphones. Node B, i.e. suboccipital cord connection node, is hold in a stable position owing to the uniform distribution of various forces that arise in the occipital region at the specified arrangement geometry of the cords and their mutual coupling, taking into account human anatomical features.
FIG. 10 shows a vector diagram of projections of the forces acting on the suboccipital cord connection node, node B. Node B is fixed through tension of the cords. Thin arrows indicate tensile forces of the cords, the total of which creates pressure on the skin. As a result, node B experiences a force of reaction of the skin and surrounding tissues, indicated by wide arrow, that seeks to move the node down, and the arising forces of friction against the cord, marked with wide solid arrow, fix the position of node B. In this model, the tension of cords below the node was neglected, as its length has been chosen for optimal and the cord is loose, has an excess length of about 9.8 cm to ensure mobility of the cords in movements of the head and neck.
Table 1 summarizes results of comparison of cord mobility and maximum cord length in headsets with different geometries.
TABLE 1Comparison of mobility and maximum length of cord in headsets with various geometryMovementRotation of head in horizontal planeTilt of head forward/backwardTilt of head sidewayHeadset typeFormulaEstimate at parameters:FormulaEstimate at parameters:FormulaEstimate at parametersHeadset with(6)R = 6.5 cm, h = 6 cm,(12)R = 6.5 cm,(24)R = 6.5 cm, h = 6 cm,two nodesD = 1 cm, α = 90° = 1.6h0 = 2 cm, D = 1 cmh0 = 2 cm αm = 45° = 0.8 radrad ΔSt = 2.9 cmΔSc = 8.6 cmΔSs = 0.6 cmLmax = 9.8 cm (see expression (14))Headset with(7)R = 6.5 cm,(18)r0 = 3 cm,(34)R = 6.5 cm, h = 6 cmsingle nodeH = 13 cmγ0 = 45°h0 = 2 cm αm = 45° = 0.8 radΔSt1 = 12.5 cmΔSc1 = 2.2 cmΔSs1 = 3.4 cmLmax 1 = {square root over (H2 + R2π2)} = 25.5 cmHeadset with(8)R = 7 cm,(19)r0 = 3 cm,R = 6.5 cm, h = 6 cmtwo side nodesH = 13 cmγ0 = 45°h0 = 2 cm αm = 45° = 0.8 radΔSt2 = 5.2 cmΔSc2 = 3 cmΔSs2 = 11 cmLmax 2 = H + Rsαm = 19.4 cm